A note on the well-posed anisotropic discrete BVPs

Anisotropic Image Sharpening via Well-Posed Sobolev Gradient Flows

We study well-posed perturbations of formally ill-posed diffusion equations which are used in image processing, such as the Perona–Malik equation. Our perturbation technique is to consider the diffusion equations as L gradient flows on integral functionals and then modify the inner product from L to a Sobolev inner product. We show that the functional differential equations obtained in this way...

The Well - Posed Problem

Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency de nition of probability; yet they may appear well posed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a de n...

Well-Posed Discrete Time Linear Systems and Their Feedbacks

In this paper we give de nitions and basic results concerning various feedback and stability properties of the linear systems built around the following system of autonomous di erence equations (xj+1 = Axj + Buj ; yj = Cxj +Duj ; j = 0; 1 2 : : : Here uj 2 U , xj 2 H and yj 2 Y (all of these are possibly in nite dimensional Hilbert spaces), and A, B, C and D are bounded linear operators. In the...

A Note on Uniqueness for Anisotropic Fluids

A Note on a Problem Posed by D . E . Knuth

We resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth’s recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth’s recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.